CBSE Questions for Class 11 Engineering Physics Mechanical Properties Of Solids Quiz 5 - MCQExams.com

When a certain weight is suspended from a long uniform wire, its length increases by $$1\ cm$$. If the same weight is suspended  from another wire of the same material and length but having a diameter half of the first one, the increase in length will be
  • $$0.5cm$$
  • $$2cm$$
  • $$4cm$$
  • $$8cm$$
A thick rope of density $$\rho$$ and length $$L$$ is hung from a rigid support. The increase in length of the rope due to its own weight is ($$Y$$ is the Young's modulus)
  • $$\dfrac {0.1}{4Y} \rho L^{2}g$$
  • $$\dfrac {1}{2Y} \rho L^{2}g$$
  • $$\dfrac {\rho L^{2}g}{Y}$$
  • $$\dfrac {\rho Lg}{Y}$$
When the tension in a metal wire is $${T}_{1}$$, its length is $${l}_{1}$$. When the tension is $${T}_{2}$$, its length is $${l}_{2}$$. The natural length of wire is
  • $$\cfrac { { T }_{ 2 } }{ { T }_{ 1 } } ({ l }_{ 1 }+{ l }_{ 2 })$$
  • $${ T }_{ 1 }{ l }_{ 1 }+{ i }_{ 2 }{ l }_{ 2 }$$
  • $$\cfrac { { { l }_{ 1 }T }_{ 2 }-{ { l }_{ 2 }T }_{ 1 } }{ { T }_{ 2 }-{ T }_{ 1 } } $$
  • $$\cfrac { { { l }_{ 1 }T }_{ 2 }+{ { l }_{ 2 }T }_{ 1 } }{ { T }_{ 2 }+{ T }_{ 1 } } $$
A wire stretched $$1mm$$ by a force of $$1kN$$. How far would a wire of the same material and length but of four times that diameter be stretched by the same force?
  • $$\dfrac {1}{2} mm$$
  • $$\dfrac {1}{4} mm$$
  • $$\dfrac {1}{8} mm$$
  • $$\dfrac {1}{16} mm$$
Bulk modulus of water is $$2\times 10^{9}N/m^{2}$$. The change in pressure required to increase the density of water by $$0.1\%$$ is
  • $$2\times 10^{9}N/{m^{2}}$$ 
  • $$2\times 10^{8}N/{m^{2}}$$
  • $$2\times 10^{6}N/{m^{2}}$$
  • $$2\times 10^{4}N/{m^{2}}$$
Each of the pictures shows four objects tied together with rubber bands being pulled to the right across a horizontal frictionless surface by a horizontal force $$F$$. All the objects have the same mass; all the rubber bands obey Hooke's law and have the same equilibrium length and the same force constant. Which of these pictures is drawn most correctly?
A ball falling in a lake of depth $$200\ m$$ shows a decrease of $$0.1\%$$ in its volume at the bottom. The bulk modulus of the elasticity of the material of the ball is (take $$g = 10\ m/s^{2})$$.
  • $$10^{9}N/m^{2}$$
  • $$2\times 10^{9}N/m^{2}$$
  • $$3\times 10^{9}N/m^{2}$$
  • $$4\times 10^{9}N/m^{2}$$
Young's modulis of brass and steel are $$10\times 10^{10} N/m$$ and $$2\times 10^{11} N/m^{2}$$, respectively. A brass wire and a steel wire of the same length are extended by $$1\ mm$$ under the same force. The radii of the brass and steel wires are $$R_{B}$ and $$R_{S}$$, respectively. Then
  • $$R_{S} = \sqrt {2} R_{B}$$
  • $$R_{S} = \dfrac {R_{B}}{\sqrt {2}}$$
  • $$R_{S} = 4R_{B}$$
  • $$R_{S} = \dfrac {R_{B}}{4}$$
A $$5\ kg$$ rod of square cross section $$5\ cm$$ on a side and $$1\ m$$ long is pulled along a smooth horizontal surface by a force applied at one end. The rod has a constant acceleration of $$2\ m/s^{2}$$. Determine the elongation in the rod. (Young's modulus of the material of the rod is $$5\times 10^{3} N/m^{9})$$.
  • Zero, as for elongation to be there, equal and opposite forces must act on the rod
  • Non-zero but cannot be determine from the given situation
  • $$4\mu m$$
  • $$16\mu m$$
Two wires of the same material and same mass are stretched by the same force. Their length are in the ratio $$2:3$$. Their elongations are in the ratio
  • $$3:2$$
  • $$2:3$$
  • $$4:9$$
  • $$9:4$$
A rubber rope of length $$8\ m$$ is hung from the ceiling of a room. What is the increase in length of rope due to its own weight? (Given : Young's modulus of elasticity of rubber $$= 5\times 106\ N/m$$ and density of rubber $$= 1.5\times 10^{3} kg/ m^{3}$$. Take $$g = 10\ m/s^{2})$$.
  • $$1.5mm$$
  • $$6mm$$
  • $$24mm$$
  • $$96mm$$
The valve $$V$$ in the bent tube is initially kept closed. Two soap bubbles $$A$$ (smaller) and $$B$$ (larger) are formed at the two open ends of the tube. $$V$$ is now opened and air can flow freely between the bubbles.

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  • There will be no change in the size of the bubbles
  • The bubbles will become of equal size
  • $$A$$ will become smaller and $$B$$ will become larger
  • The sizes of $$A$$ and $$B$$ will be interchanged
Two wires $$A$$ and $$B$$ have the same cross section and are made of the same material, but the length of wire $$A$$ is twice that of $$B$$. Then, for a given load.
  • The extension of $$A$$ will be twice that of $$B$$
  • The extensions of $$A$$ and $$B$$ will be equal
  • The strain in $$A$$ will be half that in $$B$$
  • The strains in $$A$$ and $$B$$ will be equal
Identical springs of steel and sopper $$(Y_s > Y_{cu})$$ are equally stretched. Then
  • less work is done on steel spring
  • less work is done on copper spring
  • equal work is done on both the springs
  • data not complete
Which of the following affects the elasticity of a substance?
  • Hammering and annealing
  • Change in temperature
  • Impurity in substance
  • All of the above
A steel wire of length $$4.7\ m$$ and cross-sectional area $$3\times 10^{-6} m^{2}$$ stretches by the same amount as a copper wire of length $$3.5\ m$$ ad cross-sectional area of $$4\times 10^{-6} m^{2}$$ under a given load. The ratio of Young's modulus of steel to that of copper is
  • $$1.8$$
  • $$3.6$$
  • $$0.6$$
  • $$8.7$$
A wire is stretched by a force $$F$$. If $$s$$ is the strain developed and $$Y$$ is Young's modulus of material of wire, then work done per unit volume is 
  • $$\displaystyle\frac{Ys^2}{2}$$
  • $$\displaystyle\frac{s^2}{2Y}$$
  • $$\displaystyle\frac{1}{2}Fs$$
  • $$\displaystyle\frac{Y}{2s^2}$$
A iron bar of length $$l$$ cm and cross section $$A$$ $$cm^2$$ is pulled by a force of $$F$$ dynes iron ends so as to produce an elongation $$\Delta l$$ cm. Which of the following statement is correct?
  • Elongation is inversely proportional to length
  • Elongation is directly proportional to cross section $$A$$
  • Elongation is inversely proportional to $$A$$
  • Elongation is directly proportional to Young's module
The longitudinal extension of any elastic material is very small. In order to have an appreciable change, the material must be in the form of 
  • thin block of any cross section
  • thick block of any cross section
  • long thin wire
  • short thin wire
A uniform plank is resting over a smooth horizontal floor and is pulled by applying a horizontal force at its one end. Which of the following statements are not correct?
  • Stress developed in plank material is maximum at the end at which force is applied and decrease linearly to zero at the other end
  • A uniform tensile stress is developed in the plank material
  • Since plank is pulled at one end only, plank starts to accelerate along direction of the force. Hence, no stress is developed in the plank material
  • None of the above
A spherical ball contracts in volume by $$0.02\%$$ when subjected to a pressure of $$100$$ atmosphere. Assuming one atmosphere $$=10^8\ Nm^{-2}$$, the bulk modulus of the material of the ball is 
  • $$0.02\times 10^5\ N/m^2$$
  • $$0.02\times 10^7\ N/m^2$$
  • $$50\times 10^7\ N/m^2$$
  • $$50\times 10^9\ N/m^2$$
The bulk modulus of a perfectly rigid body is 
  • infinity
  • zero
  • some finite value
  • non-zero constant
A metal rod of Young's modulus $$2\times 10^{10}Nm^{-2}$$ undergoes an elastic strain of $$0.06\%$$. The energy per unit volume stored in $$Jm^{-3}$$ is 
  • $$3600$$
  • $$7200$$
  • $$10800$$
  • $$14400$$
There are two wires of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be
  • $$1:1$$
  • $$2:1$$
  • $$1:2$$
  • $$4:1$$
Uniform rod of mass $$m$$, length $$l$$, area of cross-section $$A$$ has Young's modulus $$Y$$. If it is hanged vertically, elongation under its own weight will be :
  • $$\displaystyle\frac{mgl}{2AY}$$
  • $$\displaystyle\frac{2mgl}{AY}$$
  • $$\displaystyle\frac{mgl}{AY}$$
  • $$\displaystyle\frac{mgY}{Al}$$
A steel ring of radius $$r$$ and cross sectional area $$A$$ is fitted onto a wooden disc of radius $$R(R>r)$$. If the Young's modulus of steel is $$Y$$, then the force with which the steel ring is expanded is 
  • $$AY(R/r)$$
  • $$AY(R-r)/r$$
  • $$(Y/A)[(R-r)/r]$$
  • $$Yr/AR$$
Two wires of same material and length but cross-sections in the ratio $$1:2$$ are used to suspend the same loads. The extensions in them will be in the ratio
  • $$1:2$$
  • $$2:1$$
  • $$4:1$$
  • $$1:4$$
The length of an iron wire is $$L$$ and area of cross-section is $$A$$. The increase in length is $$l$$ on applying the force $$F$$ on its two ends. Which of the statement is correct?
  • Increase in length is inversely proportional to its length
  • Increase in length is proportional to area of cross-section
  • Increase in length is inversely proportional to area of cross-section
  • Increase in length is proportional to Young's modulus.
From a steel wire of density $$\rho$$ is suspended a brass block of density $$\rho_b$$. The extension of steel wire comes to $$e$$. If the brass block is now fully immersed in a liquid of density $$\rho_{\gamma}$$ the extension becomes $$e'$$. The ratio $$\dfrac{e}{e^{'}}$$ will be 
  • $$\displaystyle\dfrac{\rho_b}{\rho_b-\rho_l}$$
  • $$\displaystyle\dfrac{\rho_b-\rho_l}{\rho_b}$$
  • $$\displaystyle\dfrac{\rho_b-\rho}{\rho_l-\rho}$$
  • $$\displaystyle\dfrac{\rho_l}{\rho_b-\rho_l}$$
A cube at temperature $$0^oC$$ is compressed equally from all sides by an external pressure $$P$$. By what amount should its temperature be raised to bring it back to the size it had before the external pressure was applied. The bulk modulus of the material of the cube is $$B$$ and the coefficient of linear expansion is $$\alpha$$.
  • $$P/B\alpha$$
  • $$P/3B\alpha$$
  • $$3\pi \alpha/ B$$
  • $$3B/P$$
$$A$$ and $$B$$ are two wires. The radius of $$A$$ is twice that of $$B$$. They are stretched by the same load. Then the stress on $$B$$ is 
  • equal to that on $$A$$
  • four times that on $$A$$
  • two times that on $$A$$
  • half that on $$A$$
When a pressure of $$100$$ atmosphere is applied on a spherical ball, then its volume reduces to $$0.01\%$$. The bulk modulus of the material of the rubber in $$dyne/cm^2$$ is :
  • $$10\times 10^{12}$$
  • $$100\times 10^{12}$$
  • $$1\times 10^{12}$$
  • $$1000\times 10^{12}$$
Two wire $$A$$ and $$B$$ are of the same material. Their lengths are in the ratio of $$1:2$$ and the diameter are in the ratio $$2:1$$. If they are pulled by the same force, then increase in length will be in the ratio of 
  • $$2:1$$
  • $$1:4$$
  • $$1:8$$
  • $$8:1$$
If a rubber ball is taken at the depth of $$200m$$ in a pool, its voulme decreases by $$0.1\%$$. If the density of the water is $$1\times 10^3kg/m^3$$ and $$g=10m/s^2$$, then the volume elasticity in $$N/m^2$$ will be
  • $$10^8$$
  • $$2\times 10^8$$
  • $$10^9$$
  • $$2\times 10^9$$
Two wires are made of the same material and have the same volume. However wire $$1$$ has cross-sectional area $$A$$ and wire $$2$$ has cross-sectional area $$3A$$. If the length of wire $$1$$ increases by $$\Delta x$$ on applying force $$F$$, how much force is needed to stretch wire $$2$$ by the same amount? 
  • $$4F$$
  • $$6F$$
  • $$9F$$
  • $$F$$
A mass m is suspended from a wire. Change in length of the wire is $$\Delta l$$. Now the same wire is stretched to double its length and the same mass is suspended from the wire. The change in length in this case will become (it is assumed that elongation in the wire is within the proportional limit)
  • $$\Delta l$$
  • $$2\Delta l$$
  • $$4\Delta l$$
  • $$8\Delta l$$
The maximum load that a wire can sustain is $$W$$. If the wire is cut to half its value, the maximum load itcan sustain is
  • $$W$$
  • $$\dfrac{w}{2}$$
  • $$\dfrac{w}{4}$$
  • $$2W$$
A uniform steel rod of cross-sectional area $$A$$ and length $$L$$ is suspended so that it hangs vertically. The stress at the middle point of the rod is :
  • $$\dfrac{1}{2}\rho gL$$
  • $$\dfrac{1}{4}\rho gL$$
  • $$\rho gL$$
  • None of these
Identify the case when an elastic metal rod does not undergo elongation:
  • it is pulled with a constant acceleration on a smooth horizontal surface
  • it is pulled with constant velocity on a rough horizontal surface
  • it is allowed to fall freely
  • all of the above
The bulk modulus of water is $$2.0 \times 10^{9} N/m^{2}$$ The pressure required to increase the density of water by $$0.1\%$$ is :
  • $$2.0\times 10^{3} N/m^{2}$$
  • $$2.0\times 10^{6} N/m^{2}$$
  • $$2.0\times 10^{5} N/m^{2}$$
  • $$2.0\times 10^{7} N/m^{2}$$
Vessel of $$1 \times 10^{-3} m^{3}$$volume contains an oi. If a pressure of $$1.2 \times 10^{5} N/m^{2}$$is applied on it, thenvolume decreases by $$0.3\times 10^{-3}m^{3}$$ . The bulk modulus of oil is
  • $$6\times 10^{10}N/m^{2}$$
  • $$4\times 10^{5}N/m^{2}$$
  • $$2\times 10^{7}N/m^{2}$$
  • $$1\times 10^{6}N/m^{2}$$
Two wires of the same material have lengths in the ratio 1:2 and their radii are in the ratio $$1:\sqrt{2}$$. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio :
  • $$2$$
  • $$\sqrt{2}:2$$
  • $$1:1$$
  • $$1:2$$
The area of cross-section of a wire of length $$1.1$$ meter is $$1\:mm^{2}$$. It is loaded with 1 kg. If Young's modulus of copper is $$1.1\times 10^{11}N/m^{2}$$, then the increase in length will be (If $$g=10\:m/s^{2}$$) :
  • $$0.01\  mm$$
  • $$0.075 \ mm$$
  • $$0.1\  mm$$
  • $$0.15\  mm$$
How much force is required to produce an increase of 0.2% in the length of a brass wire of diameter 0.6 mm? [Young modulus for brass $$=0.9\times 10^{11}N/m^{2}$$]:-
  • Nearly 17 N
  • Nearly 34 N
  • Nearly 51 N
  • Nearly 68 N
The Young's modulus of a rubber string $$8\  cm$$ long and density $$1.5\ kg/m^ {3}$$ is $$5\times 10^{8}N/m^{2},$$ is suspending on the ceiling in a room. The increase in the length due to its own weight will be:
  • $$9.6\times 10^{-5}\ m$$
  • $$9.6\times 10^{-11}\ m$$
  • $$9.6\times 10^{-3}\ m$$
  • $$9.6\ m$$
On increasing the length by $$0.5 mm$$ in a steel wire of length $$2 m$$ and area of cross-section $$2\:cm^{2}$$, the force required is [$$Y$$ for steel $$=2.2\times 10^{11}N/m^{2}$$]:
  • $$1.1\times 10^{5}\:N$$
  • $$1.1\times 10^{4}\:N$$
  • $$1.1\times 10^{3}\:N$$
  • $$1.1\times 10^{2}\:N$$
A force of $$10^{3}$$ N stretches the length of a hanging wire by $$1$$ millimeter. The force required to stretch a wire of same material and length but having four times the diameter by $$1$$ millimeter is :
  • $$4\times 10^{3}$$ N
  • $$16\times 10^{3}$$ N
  • $$\displaystyle \frac{1}{4}\times 10^{3}$$ N
  • $$\displaystyle \frac{1}{16}\times 10^{3}$$ N
A fixed volume of iron is drawn into a wire of length $$l$$. The extension produced in this wire by a constant force $$F$$ is proportional to :
  • $$\displaystyle \dfrac{1}{l^{2}}$$
  • $$\displaystyle \dfrac{1}{l}$$
  • $$l^{2}$$
  • $$l$$
The diameter of a brass rod is 4 mm and Young's modulus of brass is $$9\times 10^{10}N/m^{2}$$. The force required to stretch by 0.1% of its length is :-
  • $$360\pi \:N$$
  • 36 N
  • $$144\pi \times 10^{3}\:N$$
  • $$36\pi \times 10^{5}\:N$$
The dimensions of two wires $$A$$ and $$B$$ are the same. But their materials are different, Their load- extension graphs are shown. If $$Y_{A}$$ and $$Y_{B}$$ are the values of Young's modulus of elasticity of $$A$$ and $$B$$ respectively then :
282045.png
  • $$Y_{A} >Y_{B}$$
  • $$Y_{A}< Y_{B}$$
  • $$Y_{A} =Y_{B}$$
  • $$Y_{B} =2Y_{A}$$
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